Constant of Proportionality and Linear Relationships

Miss Jacobson explains how to find the constant of proportionality in proportional graphs. She uses two examples: water usage over time and hiking distance over time. The video demonstrates setting up a table to identify patterns and calculate the constant of proportionality, emphasizing the use of the formula y = kx. The first example shows a straightforward calculation with whole numbers, while the second involves rational numbers, requiring the use of a y/x column to determine the constant.

What is the constant of proportionality in a proportional graph?

• The difference between x and y values

• The number you multiply x by to get y

• The y-intercept of the graph

• The slope of the graph

How can you find the constant of proportionality using a table?

• By dividing y by x for each pair

• By adding x and y values

• By multiplying x and y values

• By subtracting x from y

What is the first step in finding the constant of proportionality?

• Find the midpoint of the graph

• Set up a table of values

• Identify the y-intercept

• Calculate the slope

In the water usage graph, what is the constant of proportionality?

• 6

• 3

• 4

• 5

What does the x variable represent in the water usage graph?

• Hours passed

• Liters of water used

• Minutes passed

• Gallons of water used

In the water usage example, how many gallons are used in 3 minutes?

• 25 gallons

• 15 gallons

• 10 gallons

• 20 gallons

What is the pattern observed in the water usage table?

• x values are doubled

• y values are five times x values

• y values are halved

• x values are subtracted from y values

What is the constant of proportionality if y = 5x?

• 5

• 1

• 10

• 0

What is the constant of proportionality if y = 3x?

• 5

• 3

• 1

• 0

In the water usage example, how many gallons are used in 7 minutes?

• 35 gallons

• 30 gallons

• 40 gallons

• 45 gallons